Question: A circle with circumference $20\pi$ has an arc with a $12^\circ$ central angle. What is the length of the arc? ${20\pi}$ ${12^\circ}$ $\color{#DF0030}{\dfrac{2}{3}\pi}$
The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{12^\circ}{360^\circ} = \dfrac{s}{20\pi}$ $\dfrac{1}{30} = \dfrac{s}{20\pi}$ $\dfrac{1}{30} \times 20\pi = s$ $\dfrac{2}{3}\pi = s$